The environmental protection regulation has become stricter and stricter all over the world, and electric appliances also have severe standards for power consumption. Therefore, a power supply usually has an energy-saving circuit to control the output mode when the load varies for reducing the circuit-switching loss to the minimum. Refer to FIG. 1. A conventional power supply comprises: a primary-side rectifier unit 11, a transformer 12, a PWM (Pulse Width Modulation) unit 15, a switch unit 13 and a feedback unit. The feedback unit is coupled to the secondary side and further comprises: a current feedback unit 141 and a voltage feedback unit 142. The primary-side rectifier unit 11 receives an external power and performs a preliminary conversion and then transfers power to the transformer 12. The transformer 12 converts power from the primary side to the secondary side. Then, the power is rectified into a stable DC output. The PWM unit 15 provides a working cycle signal to control the switch unit 13 to determine whether to turn on or turn off the primary side of the transformer 12. The PWM unit 15 can adjust the duty cycle ratio of the working cycle signal according to the feedback signal provided by the current feedback unit 141 and the voltage feedback unit 142. However, the adjustment of duty cycle ratio has its limit. Therefore, the industry developed a variable-frequency energy-saving circuit and a cycle-skipping energy-saving circuit. However, the cycle modification in a variable-frequency or cycle-skipping energy-saving circuit usually causes voltage variation, as shown in FIG. 2. The sudden increase or decrease of frequency results in the upward or downward fluctuation of voltage, which influences the stability of power output. A U.S. Pat. No. 6,212,079 proposed a variable-frequency energy-saving technology—“Method and Apparatus for Improving Efficiency in a Switching Regulator at Light Loads”, which can adjust the operational frequency of a switch unit. Therefore, the conventional technology not only can adjust the duty cycle ratio of the working cycle signal of the switch unit but also can adjust the frequency of the working cycle signal. Thereby, the conventional technology can reduce the loss of switching the switch unit. Further, output loss can also be reduced. In a variable-frequency energy-saving circuit, frequency varies with load. Thus, frequency may change anytime and is hard to synchronize with the power-factor regulation circuit or the PWM circuit of the power supply. Non-synchronicity generates beat-frequency noise, or even audible noise of frequency variation. Besides, a variable-frequency energy-saving circuit is hard to integrate with a power-factor regulation circuit or a PWM circuit. A U.S. Pat. No. 7,054,169 proposed a cycle-skipping energy-saving technology—“Switched-Mode Power Supply Supporting Burst-Mode Operation”, wherein the cycles of a transformer are divided into a normal mode and a burst mode. Under a common heavy load, the output power sensing unit detects the variation of the load to modulate the pulse width. When the load is decreased to a given value, the conventional technology maintains the original pulse width and skips over the pulses of some cycles to control the circuit to reduce loss via decreasing pulse width or increasing the length of sheltered cycles. The burst-mode technology has an obvious disadvantage—the frequency-shift noise, which is generated by low-frequency interference during sheltered cycles, becomes greater with decreasing frequency; the user can clear hear frequency-shift noise in a light load. Besides, sudden change of load results in sudden decrease of output voltage and a flexuous voltage waveform generated by the over-response circuit (as shown in FIG. 6 and FIG. 8 in the specification of the abovementioned patent). Therefore, the conventional technology has the disadvantages of non-synchronicity and obvious low-frequency/beat-frequency noise. Thus, the abovementioned problems should be overcome to improve the integration with other circuits and decrease users' discomfort.